Submission date: 30 June 2015.

Abstract:

Let N=(R, +, ⋅, <, ...) be an o-minimal expansion of the standard structure of a real closed field R. Let G be a definable group and X a definable proper definable G set. We prove that X has only finitely many orbit types. We also prove equivariant definable Tietze extension theorem.

Mathematics Subject Classification: 14P10, 57S10, 03C64.

Keywords and phrases: Finiteness of orbit types, equivariant definable Tietze extension theorem, o-minimal, real closed fields.

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